Question

14. What is the interest rate of a 4-year, annual $1,000 annuity with present value of $3,500? A. 3.85 percent B. 5.56 percent C. 8.84 percent D. 9.70 percent 15. You wish to buy a $15,000 car. The dealer offers you a 4-year loan with a 9 percent APR What are the monthly payments? A. $260.78 B. $312.50 C. $373.28 D. $3,820.56 16. You are planning to make monthly deposits of $330 into a retirement account that pays 8 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement account be in 25 years? I. $313838 2. $289499 3. $24124 4. $285992 17. What is the EAR of 14.9 percent compounded continuously? 1. 15.59 percent 2. 15.62 percent 3. 15.69 percent 4. 15.84 percent 5. 16.07 percent 18. Phil purchased a car today at a price of $8,500. He paid $300 down in cash and financed the balance for 36 months at 5.75 percent, compounded monthly. What is the amount of each monthly loan payment? 1. $248.53 2. $270.23 3. S318.47 4. $305.37 5. $257.62

Answer 1

14.

Annual Annuity Amount = P = $1000

Present Value = PV = $3500

Number of years = n = 4

Let interest Rate = r

Hence, PV = P/(1+r) + P/(1+r)² +....+ P/(1+r)ⁿ = P[1- (1+r)^-n]/r

=> 3500 = 1000[1- (1+r)^-4]/r

=> [1- (1+r)^-4]/r = 3.5

Using iterative calculation approach, r = 0.0556 or 5.56%

15.

Loan Amount P = $15000

Interest Rate = 9% or 0.09/12 monthly

Number of payment periods = n = 4*12 = 48 months

Let monthly payments made be X

Hence, the sum of present value of monthly payments must be equal to the value of the loan amount

=> X/(1+r) + X/(1+r)² +....+ X/(1+r)^N = P

=> X[1- (1+r)^-N]/r = P

=> X = rP(1+r)^N/[(1+r)^N-1]

Hence, Monthly Payments =  rP(1+r)^N/[(1+r)^N-1]

= 15000*( 0.09/12)*(1+ 0.09/12)⁴⁸/((1+ 0.09/12)⁴⁸-1) = $373.28

16.

Amount Deposited each month = P = $330

Monthly Interest rate = r = 0.08/12

Number of payments made = 25*12 = 300

Hence, Future Value = FV = P(1+r)^n-1 +....+ P(1+r)² + P(1+r) + P = P[(1+r)ⁿ -1]/r = 330[(1+0.08/12)³⁰⁰ -1]/(0.08/12) = $313,838

17.

Interest rate = r = 14.9%

Number of years = t = 1

EAR = e^rt - 1 = e^0.149*1 - 1 = 0.1607 or 16.07%

18.

Downpayment = $300

Loan Amount P = $8500 - 300 = $8200

Interest Rate = 5.75% or 0.0575/12 monthly

Number of payment periods = n = 36 months

Let monthly payments made be X

Hence, the sum of present value of monthly payments must be equal to the value of the loan amount

=> X/(1+r) + X/(1+r)² +....+ X/(1+r)^N = P

=> X[1- (1+r)^-N]/r = P

=> X = rP(1+r)^N/[(1+r)^N-1]

Hence, Monthly Payments =  rP(1+r)^N/[(1+r)^N-1]

= 8200*( 0.0575/12)*(1+ 0.0575/12)³⁶/((1+0.0575/12)³⁶-1) = $248.53